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Artificial compressibility SAV ensemble algorithms for the incompressible Navier-Stokes equations

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Abstract

This report presents two scalar auxiliary variable (SAV) ensemble algorithms based on artificial compressibility (AC) for fast computation of incompressible flow ensembles. We combine and exploit three numerical techniques: ensemble timestepping, SAV, AC, to design extremely efficient and fast algorithms for the computation of a (possibly large) Navier-Stokes flow ensemble. The proposed numerical algorithms feature that (1) all ensemble members share a common constant coefficient matrix allowing the use of efficient block solvers to significantly reduce required computational cost and (2) the computation of the velocity and the pressure is decoupled, and the pressure can be updated directly without solving a Poisson equation, further reducing the overall computational cost. We prove both algorithms are long time stable under a parameter fluctuation condition, without any timestep constraints. Extensive numerical tests are also presented to demonstrate the efficiency and effectiveness of the ensemble algorithms.

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Funding

Nan Jiang was partially supported by the US National Science Foundation grants DMS-1720001, DMS-2120413, and DMS-2143331. Huanhuan Yang was supported in part by the National Natural Science Foundation of China under grant 11801348, the key research projects of general universities in Guangdong Province (grant 019KZDXM034), and the basic research and applied basic research projects in Guangdong Province (Projects of Guangdong, Hong Kong and Macao Center for Applied Mathematics, grant 2020B1515310018).

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Authors and Affiliations

  1. Department of Mathematics, University of Florida, 32611, Gainesville, FL, USA

    Nan Jiang

  2. Department of Mathematics, Shantou University, 515063, Guangdong, China

    Huanhuan Yang

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  1. Nan Jiang
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Jiang, N., Yang, H. Artificial compressibility SAV ensemble algorithms for the incompressible Navier-Stokes equations. Numer Algor 92, 2161–2188 (2023). https://doi.org/10.1007/s11075-022-01382-z

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